Bounds and Maxima for the Workload in a Multiclass Orbit Queue
In this research, a single-server <i>M</i>-class retrial queueing system (orbit queue) with constant retrial rates and Poisson inputs is considered. The main purpose is to construct the upper and lower bounds of the stationary workload in this system expressed via the stationary workload...
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| Format: | Article |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/3/564 |
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| author | Evsey V. Morozov Irina V. Peshkova Alexander S. Rumyantsev |
| author_facet | Evsey V. Morozov Irina V. Peshkova Alexander S. Rumyantsev |
| author_sort | Evsey V. Morozov |
| collection | DOAJ |
| description | In this research, a single-server <i>M</i>-class retrial queueing system (orbit queue) with constant retrial rates and Poisson inputs is considered. The main purpose is to construct the upper and lower bounds of the stationary workload in this system expressed via the stationary workloads in the classical <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>/</mo><mi>G</mi><mo>/</mo><mn>1</mn></mrow></semantics></math></inline-formula> systems where the service time has <i>M</i>-component mixture distributions. This analysis is applied to establish the extreme behaviour of stationary workload in the retrial system with Pareto service-time distributions for all classes. |
| first_indexed | 2024-03-11T09:34:59Z |
| format | Article |
| id | doaj.art-0518b657d0bc41a49e3138c58be48832 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:34:59Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0518b657d0bc41a49e3138c58be488322023-11-16T17:21:24ZengMDPI AGMathematics2227-73902023-01-0111356410.3390/math11030564Bounds and Maxima for the Workload in a Multiclass Orbit QueueEvsey V. Morozov0Irina V. Peshkova1Alexander S. Rumyantsev2Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, RussiaDepartment of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, RussiaDepartment of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, RussiaIn this research, a single-server <i>M</i>-class retrial queueing system (orbit queue) with constant retrial rates and Poisson inputs is considered. The main purpose is to construct the upper and lower bounds of the stationary workload in this system expressed via the stationary workloads in the classical <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>/</mo><mi>G</mi><mo>/</mo><mn>1</mn></mrow></semantics></math></inline-formula> systems where the service time has <i>M</i>-component mixture distributions. This analysis is applied to establish the extreme behaviour of stationary workload in the retrial system with Pareto service-time distributions for all classes.https://www.mdpi.com/2227-7390/11/3/564finite mixture distributionretrial systemextremal index |
| spellingShingle | Evsey V. Morozov Irina V. Peshkova Alexander S. Rumyantsev Bounds and Maxima for the Workload in a Multiclass Orbit Queue Mathematics finite mixture distribution retrial system extremal index |
| title | Bounds and Maxima for the Workload in a Multiclass Orbit Queue |
| title_full | Bounds and Maxima for the Workload in a Multiclass Orbit Queue |
| title_fullStr | Bounds and Maxima for the Workload in a Multiclass Orbit Queue |
| title_full_unstemmed | Bounds and Maxima for the Workload in a Multiclass Orbit Queue |
| title_short | Bounds and Maxima for the Workload in a Multiclass Orbit Queue |
| title_sort | bounds and maxima for the workload in a multiclass orbit queue |
| topic | finite mixture distribution retrial system extremal index |
| url | https://www.mdpi.com/2227-7390/11/3/564 |
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